A trailer dropped earlier this week showing Fiennes, 46, as Jackson, appearing to be wearing a prosthetic nose.
Paris Jackson, Michael's daughter, wrote Wednesday on Twitter, "i'm so incredibly offended by it, as i'm sure plenty of people are as well, and it honestly makes me want to vomit."
She added, "where is the respect? they worked through blood sweat and tears for ages to create such profound and remarkable legacies. shameful portrayal."
Sky Arts responded earlier this morning with a series of tweets.
"We have taken the decision not to broadcast Elizabeth, Michael & Marlon, a 30min episode from the Sky Arts Urban Myths series," the message began. "This decision was taken in light of the concerns expressed by Michael Jackson’s immediate family."
The statement on social media continued, "We set out to take a light-hearted look at reportedly true events & never intended to cause any offence. Joseph Fiennes fully supports our decision."
Paris wasn't the only Jackson family member to express disgust with the portrayal.
"Unfortunately this is what my family has to deal with. No words could express the blatant disrespect," Michael's nephew, Taj Jackson, also wrote Wednesday.
Fiennes, who the network said backed the decision to pull the episode, had defended the portrayal, saying it was "imagination."
"I deal in imagination, so I don't think imagination should have rules stamped on them. If it promotes stereotyping, then it's wrong. I made a distinction that the Jackson project doesn't do that," he told The Associated Press last year.
Michael Jackson died in 2009 at his home in California.